Final answer:
A larger sample size results in a more accurate estimate of the population mean because it decreases the standard error of the sample mean and enhances the reliability of statistical results.
Step-by-step explanation:
The advantage of a larger sample size when estimating the population mean is that it leads to an increase in the accuracy of the estimate. When we use a larger sample, the law of large numbers implies that the sample mean will be closer to the population mean, which is the true mean we're attempting to estimate. This is because a larger sample size tends to decrease the standard error, which quantifies the variability of the sample mean around the population mean.
A practical example of the effect of sample size would be taking repeated samples of size 100 from a population; due to the reduced standard error, these sample means are expected to be much closer to the population mean compared to sample means from smaller samples. Thus, statistical results derived from larger samples are generally more reliable and can lead to more precise confidence intervals, which are ranges that probably contain the population mean.
For probabilities and relative frequencies, it's standard practice to round answers to four decimal places, providing enough precision for most statistical work while avoiding excessive rounding that can lead to unreliable figures.